Cadences#

Notebook settings
-----------------

CORPUS_PATH: '/home/runner/work/workflow_deployment/beethoven_piano_sonatas'

Data and software versions
--------------------------

Data repo 'beethoven_piano_sonatas' @ 0dd51b2
dimcat version 0.3.0
ms3 version 2.2.1

dataset = dc.Dataset()
dataset.load(directory=CORPUS_PATH, parse_tsv=False)

[annotated|all|default]
All corpora
-----------
View: This view is called 'annotated'. It 
	- excludes pieces that are not contained in the metadata,
	- filters out file extensions requiring conversion (such as .xml),
	- excludes review files and folders, and
	- includes only facets containing 'expanded'.

                             has     active expanded       
                        metadata       view detected parsed
corpus                                                     
beethoven_piano_sonatas      yes  annotated       64     64

11/12 facets are excluded from this view.

N = 64 annotated pieces, 64 parsed dataframes.

Metadata#

all_metadata = dataset.data.metadata()
assert len(all_metadata) > 0, "No pieces selected for analysis."
print(f"Concatenated 'metadata.tsv' files cover {len(all_metadata)} of the {dataset.data.count_pieces()} scores.")
all_metadata.reset_index(level=1).groupby(level=0).nth(0).iloc[:,:20]

Concatenated 'metadata.tsv' files cover 64 of the 64 scores.

	piece	TimeSig	KeySig	last_mc	last_mn	length_qb	last_mc_unfolded	last_mn_unfolded	length_qb_unfolded	volta_mcs	all_notes_qb	n_onsets	n_onset_positions	guitar_chord_count	form_label_count	label_count	annotated_key	harmony_version	annotators	reviewers
corpus
beethoven_piano_sonatas	01-1	1: 2/2	1: -4	154	152	608.0	308	304	1216.0		1476.0	1679	985	0	0	241	f	2.3.0	Lars & Ya-Chuan (2.2.0), John Heilig (2.3.0)	AN

All annotation labels from the selected pieces#

all_labels = dataset.data.get_facet('expanded')

print(f"{len(all_labels.index)} hand-annotated harmony labels:")
all_labels.iloc[:20].style.apply(color_background, subset="chord")

21962 hand-annotated harmony labels:

			mc	mn	quarterbeats	quarterbeats_all_endings	duration_qb	mc_onset	mn_onset	timesig	staff	voice	label	alt_label	globalkey	localkey	pedal	chord	special	numeral	form	figbass	changes	relativeroot	cadence	phraseend	chord_type	globalkey_is_minor	localkey_is_minor	chord_tones	added_tones	root	bass_note	pedalend
corpus	piece	i
beethoven_piano_sonatas	01-1	0	1	0	0	0	9.000000	0	3/4	2/2	2	1	f.i{	nan	f	i	nan	i	nan	i	nan	nan	nan	nan	nan	{	m	True	True	(0, -3, 1)	()	0	0	nan
		1	4	3	9	9	8.000000	0	0	2/2	2	1	V65	nan	f	i	nan	V65	nan	V	nan	65	nan	nan	nan	nan	Mm7	True	True	(5, 2, -1, 1)	()	1	5	nan
		2	6	5	17	17	4.000000	0	0	2/2	2	1	i	nan	f	i	nan	i	nan	i	nan	nan	nan	nan	nan	nan	m	True	True	(0, -3, 1)	()	0	0	nan
		3	7	6	21	21	4.000000	0	0	2/2	2	1	#viio6	nan	f	i	nan	#viio6	nan	#vii	o	6	nan	nan	nan	nan	o	True	True	(2, -1, 5)	()	5	2	nan
		4	8	7	25	25	2.000000	0	0	2/2	2	1	i6	nan	f	i	nan	i6	nan	i	nan	6	nan	nan	nan	nan	m	True	True	(-3, 1, 0)	()	0	-3	nan
		5	8	7	27	27	2.000000	1/2	1/2	2/2	2	1	iio6	nan	f	i	nan	iio6	nan	ii	o	6	nan	nan	nan	nan	o	True	True	(-1, -4, 2)	()	2	-1	nan
		6	9	8	29	29	1.000000	0	0	2/2	2	1	V(4)}	nan	f	i	nan	V(4)	nan	V	nan	nan	4	nan	nan	}	M	True	True	(1, 0, 2)	()	1	1	nan
		7	9	8	30	30	2.000000	1/4	1/4	2/2	2	1	V\|HC	nan	f	i	nan	V	nan	V	nan	nan	nan	nan	HC	nan	M	True	True	(1, 5, 2)	()	1	1	nan
		8	9	8	32	32	9.000000	3/4	3/4	2/2	2	1	v{	nan	f	i	nan	v	nan	v	nan	nan	nan	nan	nan	{	m	True	True	(1, -2, 2)	()	1	1	nan
		9	12	11	41	41	4.000000	0	0	2/2	2	1	III.IVM2	ii7(2)	f	III	nan	IVM2	nan	IV	M	2	nan	nan	nan	nan	MM7	True	False	(4, -1, 3, 0)	()	-1	4	nan
		10	13	12	45	45	4.000000	0	0	2/2	2	1	ii7	nan	f	III	nan	ii7	nan	ii	nan	7	nan	nan	nan	nan	mm7	True	False	(2, -1, 3, 0)	()	2	2	nan
		11	14	13	49	49	4.000000	0	0	2/2	2	1	V43	nan	f	III	nan	V43	nan	V	nan	43	nan	nan	nan	nan	Mm7	True	False	(2, -1, 1, 5)	()	1	2	nan
		12	15	14	53	53	4.000000	0	0	2/2	2	1	I	nan	f	III	nan	I	nan	I	nan	nan	nan	nan	nan	nan	M	True	False	(0, 4, 1)	()	0	0	nan
		13	16	15	57	57	1.000000	0	0	2/2	2	1	ii6(2)	nan	f	III	nan	ii6(2)	nan	ii	nan	6	2	nan	nan	nan	m	True	False	(-1, 3, 4)	()	2	-1	nan
		14	16	15	58	58	1.000000	1/4	1/4	2/2	2	1	ii6	nan	f	III	nan	ii6	nan	ii	nan	6	nan	nan	nan	nan	m	True	False	(-1, 3, 2)	()	2	-1	nan
		15	16	15	59	59	2.000000	1/2	1/2	2/2	2	1	V65/V	nan	f	III	nan	V65/V	nan	V	nan	65	nan	V	nan	nan	Mm7	True	False	(6, 3, 0, 2)	()	2	6	nan
		16	17	16	61	61	3.000000	0	0	2/2	2	1	V\|HC}	nan	f	III	nan	V	nan	V	nan	nan	nan	nan	HC	}	M	True	False	(1, 5, 2)	()	1	1	nan
		17	17	16	64	64	1.000000	3/4	3/4	2/2	2	1	I6{	nan	f	III	nan	I6	nan	I	nan	6	nan	nan	nan	{	M	True	False	(4, 1, 0)	()	0	4	nan
		18	18	17	65	65	1.000000	0	0	2/2	2	1	ii6(2)	nan	f	III	nan	ii6(2)	nan	ii	nan	6	2	nan	nan	nan	m	True	False	(-1, 3, 4)	()	2	-1	nan
		19	18	17	66	66	1.000000	1/4	1/4	2/2	2	1	ii6	nan	f	III	nan	ii6	nan	ii	nan	6	nan	nan	nan	nan	m	True	False	(-1, 3, 2)	()	2	-1	nan

Filtering out pieces without cadence annotations#

hascadence = dc.HasCadenceAnnotationsFilter().process_data(dataset)
assert () in hascadence.indices and len(hascadence.indices[()]) > 0, "No cadences found."
print(f"Before: {len(dataset.indices[()])} pieces; after removing those without cadence labels: {len(hascadence.indices[()])}")

Before: 64 pieces; after removing those without cadence labels: 64

Show corpora containing pieces with cadence annotations#

grouped_by_corpus = dc.CorpusGrouper().process_data(hascadence)
corpora = {group[0]: f"{len(ixs)} pieces" for group, ixs in  grouped_by_corpus.indices.items()}
print(f"{len(corpora)} corpora with {sum(map(len, grouped_by_corpus.indices.values()))} pieces containing cadence annotations:")
corpora

1 corpora with 64 pieces containing cadence annotations:

{'beethoven_piano_sonatas': '64 pieces'}

All annotation labels from the selected pieces#

all_labels = hascadence.get_facet('expanded')

print(f"{len(all_labels.index)} hand-annotated harmony labels:")
all_labels.iloc[:10, 13:].style.apply(color_background, subset="chord")

21787 hand-annotated harmony labels:

			localkey	pedal	chord	special	numeral	form	figbass	changes	relativeroot	cadence	phraseend	chord_type	globalkey_is_minor	localkey_is_minor	chord_tones	added_tones	root	bass_note	pedalend
corpus	fname	interval
beethoven_piano_sonatas	01-1	[0.0, 9.0)	i	nan	i	nan	i	nan	nan	nan	nan	nan	{	m	True	True	(0, -3, 1)	()	0	0	nan
		[9.0, 17.0)	i	nan	V65	nan	V	nan	65	nan	nan	nan	nan	Mm7	True	True	(5, 2, -1, 1)	()	1	5	nan
		[17.0, 21.0)	i	nan	i	nan	i	nan	nan	nan	nan	nan	nan	m	True	True	(0, -3, 1)	()	0	0	nan
		[21.0, 25.0)	i	nan	#viio6	nan	#vii	o	6	nan	nan	nan	nan	o	True	True	(2, -1, 5)	()	5	2	nan
		[25.0, 27.0)	i	nan	i6	nan	i	nan	6	nan	nan	nan	nan	m	True	True	(-3, 1, 0)	()	0	-3	nan
		[27.0, 29.0)	i	nan	iio6	nan	ii	o	6	nan	nan	nan	nan	o	True	True	(-1, -4, 2)	()	2	-1	nan
		[29.0, 30.0)	i	nan	V(4)	nan	V	nan	nan	4	nan	nan	}	M	True	True	(1, 0, 2)	()	1	1	nan
		[30.0, 32.0)	i	nan	V	nan	V	nan	nan	nan	nan	HC	nan	M	True	True	(1, 5, 2)	()	1	1	nan
		[32.0, 41.0)	i	nan	v	nan	v	nan	nan	nan	nan	nan	{	m	True	True	(1, -2, 2)	()	1	1	nan
		[41.0, 45.0)	III	nan	IVM2	nan	IV	M	2	nan	nan	nan	nan	MM7	True	False	(4, -1, 3, 0)	()	-1	4	nan

Metadata#

dataset_metadata = hascadence.data.metadata()
hascadence_metadata = dataset_metadata.loc[hascadence.indices[()]]
hascadence_metadata.index.rename('dataset', level=0, inplace=True)
hascadence_metadata.head()

		TimeSig	KeySig	last_mc	last_mn	length_qb	last_mc_unfolded	last_mn_unfolded	length_qb_unfolded	volta_mcs	all_notes_qb	...	ambitus	imslp	musicbrainz	viaf	wikidata	originalFormat	staff_1_ambitus	staff_1_instrument	staff_2_ambitus	staff_2_instrument
dataset	piece
beethoven_piano_sonatas	01-1	1: 2/2	1: -4	154	152	608.0	308	304	1216.0		1476.00	...	32-89 (Ab1-F6)	https://imslp.org/wiki/Klaviersonaten_(Beethov...	https://musicbrainz.org/work/a78520e0-0211-3b5...	https://viaf.org/viaf/179625665	https://www.wikidata.org/wiki/Q145813	xml	51-89 (Eb3-F6)	piano	32-73 (Ab1-Db5)	piano
	01-2	1: 3/4	1: -1	62	61	183.0	124	122	366.0		526.17	...	31-89 (G1-F6)	https://imslp.org/wiki/Klaviersonaten_(Beethov...	https://musicbrainz.org/work/bea1b893-2732-33a...	https://viaf.org/viaf/179625665	https://www.wikidata.org/wiki/Q145813	xml	43-89 (G2-F6)	piano	31-77 (G1-F5)	piano
	01-3	1: 3/4	1: -4, 43: -1	77	73	219.0	196	186	558.0		565.50	...	31-85 (G1-Db6)	https://imslp.org/wiki/Klaviersonaten_(Beethov...	https://musicbrainz.org/work/2bd7e1ea-c696-3be...	https://viaf.org/viaf/179625665	https://www.wikidata.org/wiki/Q145813	mxl	53-85 (F3-Db6)	Piano	31-74 (G1-D5)	Piano
	01-4	1: 2/2	1: -4	199	196	790.0	392	390	1560.0	[[[57, 58], [59, 60, 61]]]	2326.83	...	31-89 (G1-F6)	https://imslp.org/wiki/Klaviersonaten_(Beethov...	https://musicbrainz.org/work/b755e900-804a-312...	https://viaf.org/viaf/179625665	https://www.wikidata.org/wiki/Q145813	mxl	50-89 (D3-F6)	Piano	31-75 (G1-Eb5)	Piano
	02-1	1: 2/4	1: 3, 127: 0, 230: 3	342	336	679.5	672	664	1336.0	[[[115, 116, 117, 118], [119, 120, 121, 122, 1...	1695.75	...	31-89 (G1-F6)	https://imslp.org/wiki/Klaviersonaten_(Beethov...	https://musicbrainz.org/work/c001a2eb-9493-327...	https://viaf.org/viaf/179221580	https://www.wikidata.org/wiki/Q145699	xml	39-89 (D#2-F6)	piano	31-76 (G1-E5)	piano

5 rows × 55 columns

mean_composition_years = hascadence_metadata.groupby(level=0).composed_end.mean().astype(int).sort_values()
chronological_order = mean_composition_years.index.to_list()
bar_data = pd.concat([mean_composition_years.rename('year'), 
                      hascadence_metadata.groupby(level='dataset').size().rename('pieces')],
                     axis=1
                    ).reset_index()
fig = px.bar(bar_data, x='year', y='pieces', color='dataset', title='Pieces contained in the dataset')
fig.update_traces(width=5)

Overall#

PAC: Perfect Authentic Cadence
IAC: Imperfect Authentic Cadence
HC: Half Cadence
DC: Deceptive Cadence
EC: Evaded Cadence
PC: Plagal Cadence

print(f"{all_labels.cadence.notna().sum()} cadence labels.")
value_count_df(all_labels.cadence)

1333 cadence labels.

	counts	%
cadence
PAC	603	0.452363
HC	406	0.304576
IAC	275	0.206302
EC	31	0.023256
DC	15	0.011253
PC	3	0.002251

px.pie(all_labels[all_labels.cadence.notna()], names="cadence", color="cadence", color_discrete_map=CADENCE_COLORS)

Per dataset#

cadence_count_per_dataset = all_labels.groupby("corpus").cadence.value_counts()
cadence_fraction_per_dataset = cadence_count_per_dataset / cadence_count_per_dataset.groupby(level=0).sum()
px.bar(cadence_fraction_per_dataset.rename('count').reset_index(), x='corpus', y='count', color='cadence',
      color_discrete_map=CADENCE_COLORS, category_orders=dict(dataset=chronological_order))

fig = px.pie(cadence_count_per_dataset.rename('count').reset_index(), names='cadence', color='cadence', values='count', 
       facet_col='corpus', facet_col_wrap=4, height=2000, color_discrete_map=CADENCE_COLORS)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_layout(**STD_LAYOUT)

Per phrase#

Number of cadences per phrase#

segmented = dc.PhraseSlicer().process_data(grouped_by_corpus)
phrases = segmented.get_slice_info()
phrase_segments = segmented.get_facet("expanded")
phrase_gpb = phrase_segments.groupby(level=[0,1,2])
local_keys_per_phrase = phrase_gpb.localkey.unique().map(tuple)
n_local_keys_per_phrase = local_keys_per_phrase.map(len)
phrases_with_keys = pd.concat([n_local_keys_per_phrase.rename('n_local_keys'),
                               local_keys_per_phrase.rename('local_keys'),
                               phrases], axis=1)
phrases_with_cadences = pd.concat([
    phrase_gpb.cadence.nunique().rename('n_cadences'),
    phrase_gpb.cadence.unique().rename('cadences').map(lambda l: tuple(e for e in l if not pd.isnull(e))),
    phrases_with_keys
], axis=1)
value_count_df(phrases_with_cadences.n_cadences, counts="#phrases")

	#phrases	%
n_cadences
1	1258	0.937407
0	59	0.043964
2	25	0.018629

n_cad = phrases_with_cadences.groupby(level='corpus').n_cadences.value_counts().rename('counts').reset_index().sort_values('n_cadences')
n_cad.n_cadences = n_cad.n_cadences.astype(str)
fig = px.bar(n_cad, x='corpus', y='counts', color='n_cadences', height=800, barmode='group',
             labels=dict(n_cadences="#cadences in a phrase"),
             category_orders=dict(dataset=chronological_order)
      )
fig.show()

Combinations of cadence types for phrases with more than one cadence#

value_count_df(phrases_with_cadences[phrases_with_cadences.n_cadences > 1].cadences)

	counts	%
cadences
(EC, PAC)	7	0.28
(HC, PAC)	5	0.20
(DC, PAC)	2	0.08
(PAC, HC)	2	0.08
(IAC, PAC)	2	0.08
(EC, IAC)	2	0.08
(DC, IAC)	1	0.04
(IAC, EC)	1	0.04
(HC, DC)	1	0.04
(EC, HC)	1	0.04
(DC, HC)	1	0.04

Positioning of cadences within phrases#

df_rows = []
y_position = 0
for ix in phrases_with_cadences[phrases_with_cadences.n_cadences > 0].sort_values('duration_qb').index:
    df = phrase_segments.loc[ix]
    description = str(ix)
    if df.cadence.notna().any():
        interval = ix[2]
        df_rows.append((y_position, interval.length, "end of phrase", description))
        start_pos = interval.left
        cadences = df.loc[df.cadence.notna(), ['quarterbeats', 'cadence']]
        cadences.quarterbeats -= start_pos
        for cadence_x, cadence_type in cadences.itertuples(index=False, name=None):
            df_rows.append((y_position, cadence_x, cadence_type, description))
        y_position += 1
    #else:
    #    df_rows.append((y_position, pd.NA, pd.NA, description))
    
data = pd.DataFrame(df_rows, columns=["phrase_ix", "x", "marker", "description"])

fig = px.scatter(data[data.x.notna()], x='x', y="phrase_ix", color="marker", hover_name="description", height=3000,
                labels=dict(marker='legend'), color_discrete_map=CADENCE_COLORS)
fig.update_traces(marker_size=5)
fig.update_yaxes(autorange="reversed")
fig.show()

Cadence ultima#

phrase_segments = segmented.get_facet("expanded")
cadence_selector = phrase_segments.cadence.notna()
missing_chord_selector = phrase_segments.chord.isna()
cadence_with_missing_chord_selector = cadence_selector & missing_chord_selector
missing = phrase_segments[cadence_with_missing_chord_selector]
expanded = ms3.expand_dcml.expand_labels(phrase_segments[cadence_with_missing_chord_selector], propagate=False, chord_tones=True, skip_checks=True)
phrase_segments.loc[cadence_with_missing_chord_selector] = expanded
print(f"Ultima harmony missing for {(phrase_segments.cadence.notna() & phrase_segments.bass_note.isna()).sum()} cadence labels.")

Ultima harmony missing for 1 cadence labels.

Ultimae as Roman numeral#

def highlight(row, color="#ffffb3"):
    if row.counts < 10:
        return [None, None, None, None]
    else:
        return ["background-color: {color};"] * 4

cadence_counts = all_labels.cadence.value_counts()
ultima_root = phrase_segments.groupby(['localkey_is_minor', 'cadence']).numeral.value_counts().rename('counts').to_frame().reset_index()
ultima_root.localkey_is_minor = ultima_root.localkey_is_minor.map({False: 'in major', True: 'in minor'})
#ultima_root.style.apply(highlight, axis=1)

fig = px.pie(ultima_root, names='numeral', values='counts', 
             facet_row='cadence', facet_col='localkey_is_minor', 
             height=1500,
             category_orders={'cadence': cadence_counts.index},
            )
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_traces(textposition='inside', textinfo='percent+label')
fig.update_layout(**STD_LAYOUT)
fig.show()

#phrase_segments.groupby(level=[0,1,2], group_keys=False).apply(lambda df: df if ((df.cadence == 'PAC') & (df.numeral == 'V')).any() else None)

Ultimae bass note as scale degree#

ultima_bass = phrase_segments.groupby(['localkey_is_minor','cadence']).bass_note.value_counts().rename('counts').reset_index()
ultima_bass.bass_note = ms3.transform(ultima_bass, ms3.fifths2sd, dict(fifths='bass_note', minor='localkey_is_minor'))
ultima_bass.localkey_is_minor = ultima_bass.localkey_is_minor.map({False: 'in major', True: 'in minor'})
#ultima_bass.style.apply(highlight, axis=1)

fig = px.pie(ultima_bass, names='bass_note', values='counts', 
             facet_row='cadence', facet_col='localkey_is_minor', 
             height=1500, 
             category_orders={'cadence': cadence_counts.index},
            )
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_traces(textposition='inside', textinfo='percent+label')
fig.update_layout(**STD_LAYOUT)
fig.show()

Chord progressions#

PACs with ultima I/i#

def remove_immediate_duplicates(l):
    return tuple(a for a, b in zip(l, (None, ) + l) if a != b)

def get_progressions(selected='PAC', last_row={}, feature='chord', dataset=None, as_series=True, remove_duplicates=False):
    """Uses the nonlocal variable phrase_segments."""
    last_row = {k: v if isinstance(v, tuple) else (v,) for k, v in last_row.items()}
    progressions = []

    for (corp, fname, *_), df in phrase_segments[phrase_segments[feature].notna()].groupby(level=[0,1,2]):
        if dataset is not None and dataset not in corp:
            continue
        if (df.cadence == selected).fillna(False).any():
            # remove chords after the last cadence label
            df = df[df.cadence.fillna(method='bfill').notna()]
            # group segments leading up to a cadence label
            cadence_groups = df.cadence.notna().shift().fillna(False).cumsum()
            for i, cadence in df.groupby(cadence_groups):
                last_r = cadence.iloc[-1]
                typ = last_r.cadence
                if typ != selected:
                    continue
                if any(last_r[feat] not in values for feat, values in last_row.items()):
                    continue
                if remove_duplicates:
                    progressions.append(remove_immediate_duplicates(cadence[feature].to_list()))
                else:
                    progressions.append(tuple(cadence[feature]))
    if as_series:
        return pd.Series(progressions, dtype='object')
    return progressions

chord_progressions = get_progressions('PAC', dict(numeral=('I', 'i')), 'chord')
print(f"Progressions for {len(chord_progressions)} cadences:")
value_count_df(chord_progressions, "chord progressions")

Progressions for 602 cadences:

	counts	%
chord progressions
(I, V7, I)	9	0.014950
(I, V43, I, V6, I, V43, I, V7, I)	6	0.009967
(V7, I)	4	0.006645
(i, i(9#74), i, i6, i, V6, V, #viio43, i6, Ger6, V(64), V, i)	4	0.006645
(I, I64, V7, viio6, I64, V7, viio6, I)	4	0.006645
...	...	...
(i, iv64, #viio7, iv64, #viio65, iv64, #viio7, V2/iv, iv6, V65/iv, iv, #viio43, V65/V, viio7/V, V(64), V7, i)	1	0.001661
(I, V2, I, V2, I, V2, I)	1	0.001661
(I, V6, I, V65, I, V6, I, V6, I, i, viio, V7, Ger6, V7, V6/vi, vi, ii6, V7, I)	1	0.001661
(#viio/vi, vi, ii, V, V/ii, ii, V7, I)	1	0.001661
(V, V65/V, V6, V, V65/V, V6, V65/ii, V43, I, V6, IV6, V, IV6, V6, I, IV, I6, viio6, I6, viio6, vi6, V6, IV6, iii6, ii6, I6, viio6, I6, viio6, vi6, V6, IV6, iii6, ii6, I6, viio6, I6, viio6, vi6, V6, IV6, iii6, ii6, I6, viio6, I)	1	0.001661

499 rows × 2 columns

numeral_progressions = get_progressions('PAC', dict(numeral=('I', 'i')), 'numeral')
value_count_df(numeral_progressions, "numeral progressions")

	counts	%
numeral progressions
(I, V, I)	10	0.016611
(I, V, V, I)	9	0.014950
(I, V, I, V, I, V, I, V, I)	8	0.013289
(I, V, I, V, V, I, V, vi, V, V, vii, V, I, V, ii, V, I)	5	0.008306
(I, V, V, IV, I, ii, V, I)	4	0.006645
...	...	...
(I, V, I, V, I, V, I, V, I, i, vii, V, vii, V, V, vi, ii, V, I)	1	0.001661
(#vii, vi, ii, V, V, ii, V, I)	1	0.001661
(I, V, I, V, V, I, V, I, V, I, V, I, V, I, V, I, V, i, V, i, V, i, V, i, V, I, V, I, V, I, V, I, vi, ii, V, I, ii, V, V, V, I)	1	0.001661
(I, V, I, V, I, V, I, I, vi, IV, vii, V, vii, I)	1	0.001661
(V, V, V, V, V, V, V, V, I, V, IV, V, IV, V, I, IV, I, vii, I, vii, vi, V, IV, iii, ii, I, vii, I, vii, vi, V, IV, iii, ii, I, vii, I, vii, vi, V, IV, iii, ii, I, vii, I)	1	0.001661

464 rows × 2 columns

numeral_prog_no_dups = numeral_progressions.map(remove_immediate_duplicates)
value_count_df(numeral_prog_no_dups)

	counts	%
(I, V, I)	28	0.046512
(I, V, I, V, I, V, I, V, I)	11	0.018272
(I, V, I, V, I)	10	0.016611
(V, I)	8	0.013289
(I, V, IV, I, ii, V, I)	6	0.009967
...	...	...
(V, i, iv, V, i)	1	0.001661
(V, i, V, i, V, i, V, I, V, I, vi, V, I)	1	0.001661
(i, iv, #vii, iv, #vii, iv, #vii, V, iv, V, iv, #vii, V, vii, V, i)	1	0.001661
(I, V, I, V, I, V, I, V, I, i, vii, V, vii, V, vi, ii, V, I)	1	0.001661
(V, I, V, IV, V, IV, V, I, IV, I, vii, I, vii, vi, V, IV, iii, ii, I, vii, I, vii, vi, V, IV, iii, ii, I, vii, I, vii, vi, V, IV, iii, ii, I, vii, I)	1	0.001661

410 rows × 2 columns

PACs ending on scale degree 1#

Scale degrees expressed w.r.t. major scale, regardless of actual key.

bass_progressions = get_progressions('PAC', dict(bass_note=0), 'bass_note')
bass_prog = bass_progressions.map(ms3.fifths2sd)
print(f"Progressions for {len(bass_progressions)} cadences:")
value_count_df(bass_prog, "bass progressions")

Progressions for 573 cadences:

	counts	%
bass progressions
(1, 5, 1)	11	0.019197
(1, 5, 5, 1)	7	0.012216
(1, 2, 1, 7, 1, 2, 1, 5, 1)	6	0.010471
(5, 1)	5	0.008726
(1, 4, 3, 7, 7, 1, 7, 6, 6, 5, 4, 4, 3, 6, 2, 5, 1)	5	0.008726
...	...	...
(1, b6, 5, 5, b6, 5, 5, 4, 5, b6, 2, b3, 4, 5, 5, 1)	1	0.001745
(7, 1, 1, 5, 4, b3, 1, 7, 1, 1, 1, 7, 1, 1, #4, 5, 5, 1, 6, 5, #4, 5, 5, 1)	1	0.001745
(1, 1, 7, 1, 2, 1, 7, b7, b6, 3, 4, 4, #4, #4, 5, 5, 1)	1	0.001745
(1, 4, 1, 4, 1, 4, 1)	1	0.001745
(5, #4, 7, 5, #4, 7, #1, 2, 1, 7, 6, 5, 6, 7, 1, 4, 3, 2, 3, 2, 1, 7, 6, 5, 4, 3, 2, 3, 2, 1, 7, 6, 5, 4, 3, 2, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1)	1	0.001745

441 rows × 2 columns

bass_prog_no_dups = bass_prog.map(remove_immediate_duplicates)
value_count_df(bass_prog_no_dups)

	counts	%
(1, 5, 1)	20	0.034904
(5, 1)	9	0.015707
(1, 5, 1, 5, 1)	7	0.012216
(1, 2, 3, 4, 5, 1)	6	0.010471
(1, 2, 1, 7, 1, 2, 1, 5, 1)	6	0.010471
...	...	...
(1, b6, 1, 4, 1, b6, 1, 4, 1, 7, 1, 7, 1)	1	0.001745
(1, 4, b3, 7, 1, 5, b6, 3, 4, 1, b2, 1, 7, #4, 5, 1, #4, 5, #4, 5, 1)	1	0.001745
(1, b3, 1, b6, 1, b6, b4, 5, b6, 6, b7, 7, 1, b2, 2, b3, 4, #4, 5, 1)	1	0.001745
(1, b6, 5, b6, 5, 4, b7, 1, 2, b3, 4, 5, 1)	1	0.001745
(5, #4, 7, 5, #4, 7, #1, 2, 1, 7, 6, 5, 6, 7, 1, 4, 3, 2, 3, 2, 1, 7, 6, 5, 4, 3, 2, 3, 2, 1, 7, 6, 5, 4, 3, 2, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1)	1	0.001745

410 rows × 2 columns

def make_sankey(data, labels, node_pos=None, margin={'l': 10, 'r': 10, 'b': 10, 't': 10}, pad=20, color='auto', **kwargs):
    if color=='auto':
        unique_labels = set(labels)
        color_step = 100 / len(unique_labels)
        unique_colors = {label: f'hsv({round(i*color_step)}%,100%,100%)' for i, label in enumerate(unique_labels)}
        color = list(map(lambda l: unique_colors[l], labels))
    fig = go.Figure(go.Sankey(
        arrangement = 'snap',
        node = dict(
          pad = pad,
          #thickness = 20,
          #line = dict(color = "black", width = 0.5),
          label = labels,
          x = [node_pos[i][0] if i in node_pos else 0 for i in range(len(labels))] if node_pos is not None else None,
          y = [node_pos[i][1] if i in node_pos else 0 for i in range(len(labels))] if node_pos is not None else None,
          color = color,
          ),
        link = dict(
          source = data.source,
          target = data.target,
          value = data.value
          ),
        ),
     )

    fig.update_layout(margin=margin, **kwargs)
    return fig

def progressions2graph_data(progressions, cut_at_stage=None):
    stage_nodes = defaultdict(dict)
    edge_weights = Counter()
    node_counter = 0
    for progression in progressions:
        previous_node = None
        for stage, current in enumerate(reversed(progression)):
            if cut_at_stage and stage > cut_at_stage:
                break
            if current in stage_nodes[stage]:
                current_node = stage_nodes[stage][current]
            else:
                stage_nodes[stage][current] = node_counter
                current_node = node_counter
                node_counter += 1
            if previous_node is not None:
                edge_weights.update([(current_node, previous_node)])
            previous_node = current_node
    return stage_nodes, edge_weights

def graph_data2sankey(stage_nodes, edge_weights):
    data = pd.DataFrame([(u, v, w) for (u, v), w in edge_weights.items()], columns = ['source', 'target', 'value'])
    node2label = {node: label for stage, nodes in stage_nodes.items() for label, node in nodes.items()}
    labels = [node2label[i] for i in range(len(node2label))]
    return make_sankey(data, labels)

def plot_progressions(progressions, cut_at_stage=None):
    stage_nodes, edge_weights = progressions2graph_data(progressions, cut_at_stage=cut_at_stage)
    return graph_data2sankey(stage_nodes, edge_weights)

Chordal roots for the 3 last stages#

plot_progressions(numeral_prog_no_dups, cut_at_stage=3)

Complete chords for the last four stages in major#

pac_major = get_progressions('PAC', dict(numeral='I', localkey_is_minor=False), 'chord')
plot_progressions(pac_major, cut_at_stage=4)

Bass degrees for the last 6 stages.#

plot_progressions(bass_prog_no_dups, cut_at_stage=7)

Bass degrees without accidentals#

def remove_sd_accidentals(t):
    return tuple(map(lambda sd: sd[-1], t))
                  
bass_prog_no_acc_no_dup = bass_prog.map(remove_sd_accidentals).map(remove_immediate_duplicates)
plot_progressions(bass_prog_no_acc_no_dup, cut_at_stage=7)

HCs ending on V#

half = get_progressions('HC', dict(numeral='V'), 'bass_note').map(ms3.fifths2sd)
print(f"Progressions for {len(half)} cadences:")
plot_progressions(half.map(remove_immediate_duplicates), cut_at_stage=5)

Progressions for 392 cadences: